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Well Quasi-orders and the Functional Interpretation

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Well-Quasi Orders in Computation, Logic, Language and Reasoning

Part of the book series: Trends in Logic ((TREN,volume 53))

Abstract

The purpose of this article is to study the role of Gödel’s functional interpretation in the extraction of programs from proofs in well quasi-order theory. The main focus is on the interpretation of Nash–Williams’ famous minimal bad sequence construction, and the exploration of a number of much broader problems which are related to this, particularly the question of the constructive meaning of Zorn’s lemma and the notion of recursion over the non-wellfounded lexicographic ordering on infinite sequences.

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Acknowledgements

In developing the ideas of this article I have benefited greatly from numerous illuminating conversations with Ulrich Berger, Paulo Oliva and Monika Seisenberger. Moreover, I am grateful to the anonymous referee, whose extremely detailed review led to a much better version of the paper.

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Correspondence to Thomas Powell .

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Powell, T. (2020). Well Quasi-orders and the Functional Interpretation. In: Schuster, P., Seisenberger, M., Weiermann, A. (eds) Well-Quasi Orders in Computation, Logic, Language and Reasoning. Trends in Logic, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-30229-0_9

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